Staircase are composed of curved step segment(s) having a curved inside radius of a first positive value and a curved outside radius of a second positive value larger than the first. Staircases are know to be either "supported", i.e., supported by the walls underneath the staircase or "free-standing", i.e., attached to the building structure only at the top and bottom of the staircase.
Staircases are constructed within a cube of space defined by plane limitations composed of three axes: X, Y, and Z. The X axis is the horizontal plane. The Y axis is the vertical plane. The Z axis is the vertical space, which is equal to the finished floor-to-ceiling height. The Z axis is unpredictable in residential construction because of the use of various floor-to-ceiling heights and variation in the thicknesses of floor finishing materials and floor structural options.
Finally, staircase are constructed within various building code limits. These building codes limit: rise (the vertical distance between adjacent steps), the variation of one rise to another in the same staircase, run (horizontal distance between steps), and variation of one run to another in the same staircase.